Tim Murray will know it's origin. If he doesn't make a comment in a day or two, I shall PM him.
Sorry M11, but I can’t help too much here. The term ‘pits’ first came about at the 1908 Grand Prix de l’ACF at Dieppe, where the organisers chose to site the replenishment depots immediately in front of the main grandstand at the start line. To avoid blocking the view of the first few rows in the grandstand, a long trench was dug in front of it and divided up into compartments for each team, where the fuel, spare tyres, etc were kept, along with a few team personnel. (In those days only the driver and his riding mechanic were allowed to work on the car during stops.)
I first became aware of the term ‘box’ in 1973, when during the Nürburgring 1,000 Km sports car race Arturo Merzario disobeyed Ferrari team orders by refusing to pit in spite of being shown the ‘BOX’ sign on his pit board for several laps. (No radios in those days.)
So Ferrari were using the term ‘box’ more than 45 years ago. My understanding is that ‘Die Boxen’ is German for ‘the pits’ but I’ve no idea how and when this originated. Perhaps some of our German contributors can help here.